Module: Argument analysis
Quote of the page
It is a mistake to confound strangeness with mystery.
- Sir Arthur Conan Doyle
It should be obvious by now that validity is about the logical connection between the premises and the conclusion. When we are told that an argument is valid, this is not enough to tell us anything about the actual truth or falsity of the premises or the conclusion. All we know is that there is a logical connection between them, that the premises entail the conclusion.
So even if we are given a valid argument, we still need to be careful before accepting the conclusion, since a valid argument might contain a false conclusion. What we need to check further is of course whether the premises are true. If an argument is valid, and all the premises are true, then it is called a sound argument. Of course, it follows from such a definition that a sound argument must also have a true conclusion. In a valid argument, if the premises are true, then the conclusion cannot be false, since by definition it is impossible for a valid argument to have true premises and a false conclusion in the same situation. So given that a sound argument is valid and has true premises, its conclusion must also be true. So if you have determined that an argument is indeed sound, you can certainly accept the conclusion.
An argument that is not sound is an unsound argument. If an argument is unsound, it might be that it is invalid, or maybe it has at least one false premise, or both.
Is it possible to have arguments of the following kinds? If so, provide an example. If not, explain why. It is particularly important to note the highlighted cases.
|Valid & sound|
|Valid & unsound|
|Invalid & sound|
|Invalid & unsound|
Are the following statements true or false? Why?
Here are some common questions from students about validity and soundness and their answers. See if you know how to answer them yourself.
(Premise) All cows are mammals.
(Conclusion) Therefore, the sun is larger than the moon.
Isn’t the conclusion a tautology?